Class 10 Practice – Level 2 – Set 2 – Some Application of Trigonometry

Total questions: 25

A kite is flying at a height of 75 m from the level ground, attached to a string inclined at a 60° to the horizontal. Find the length of the string assuming that there is no slack in it.

Topic: Properties of Length

25.6 m

35.6 m

45.2 m

86.6 m

None

From a point on the ground 40 m away from the foot of a tower, the angle of elevation of the top of the tower is 60°. The angle of elevation of the top of a water tank (on the top of the tower) is 45°. Find the height of the tower.

Topic: Height Using Angle of Elevation

23.1 m

36.2 m

53.3 m

56.1 m

None

The angle of elevation of the top of an unifinished tower at a distance of 75 m from its base is 30°. How much higher must be tower be raised so that the angle of elevation of its top at the same point may be 60°?

Topic: Angle of Elevation

86.6 m

56.4 m

56.6 m

44.5 m

None

Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point P between them on the road, the angle of elevation of the top of one pole is 60° and the angle of depression from the top of another pole at P is 30°. Find the height of each pole.

Topic: Angles of Elevation and Depression

20√3 m

40√3 m

60√3 m

50√3 m

None

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6 m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 60°. Find the height of the tower. [Use √3=1.732]

Topic: Properties of Height

3 m

4 m

10 m

60 m

None

If the length of the shadow of a tree is decreasing then the angle of elevation is:

Topic: Angle of Elevation

Decreasing

Increasing

No change

None of the above

None

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 30 meters away from the bank, he finds the angle of elevation to be 30° . Find the width of the river.(in meters) [Take √3 =1.732.]

Topic: Angle of Elevation

30 m

60 m

15 m

20 m

None

A spherical balloon of radius r subtends an angle θ at the eye of an observer. If the angle of elevation of its centre is ϕ, find the height of the centre of the balloon.

Topic: Properties of Height

330(3 + √3)m

30(3 + √3)m

60(3 + √3)m

50(3 + √3)m

None

From the top of a cliff 20 m high, the angle of elevation of the top of a tower is found to be equal to the angle of depression of the foot of the tower. Then height of the tower(in m) will be:

Topic: Height Using Angle of Elevation

None

10.

Find the angle of elevation of the sun when the shadow of a pole h meters high is √3h meters long.

Topic: Angle of Elevation

40°

30°

15°

None

11.

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then find the height of the wall.

Topic: Height using Trigonometry

6.5 m

8.2 m

6.3 m

7.5 m

None

12.

If the height of a vertical pole is equal to the length of its shadow on the ground, the angle of elevation of the sun is:

Topic: Angle of Elevation

40°

50°

60°

90°

None

13.

A pole 6 m high casts a shadow 2√3 m long on the ground, then the sun's elevation is :

Topic: Angle of Elevation

60°

40°

90°

30°

None

14.

An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower the eye of the observer.

Topic: Angle of Elevation

90°

45°

30°

60°

None

15.

A bridge across a river makes an angle of 45∘ with the river banks as shown in the figure. If the length of the bridge across the river is 100 m, then find the width of the river.

Topic: Properties of Width

50√2 m

60√2 m

70√2 m

40√2 m

None

16.

An observer, 1.7 m tall, is 20√3 m away from a tower. The angle of elevation from the eye of observer to the top of tower is 30°. Find the height of tower.

Topic: Height using Trigonometry

21.7 m

31.7 m

41.9 m

21.8 m

None

17.

From the top of a tower of height 50 m, the angles of depression of the top and bottom of a pole are 30° and 45° respectively. Find the height of the pole.

Topic: Height using Angles of Depression

41.13 m

36.13 m

22.13 m

21.13 m

None

18.

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30° .

Topic: Properties of Height

20 m

10 m

25 m

15 m

None

19.

A kite is flying, attached to a thread which is 165 m long. The thread makes an angle of 30° with the ground. Find the height of the kite from the ground, assuming that there is no slack in the thread.

Topic: Properties of Height

65.2 m

25.3 m

60.2 m

82.5 m

None

20.

The ratio of the length of a rod and its shadow is 1: $\displaystyle \dfrac{1}{{\sqrt{3}}}$ . What is the angle of elevation of the source of light?

Topic: Angle of Elevation

30°

60°

35°

40°

None

21.

If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation of the sun?

Topic: Angle of Elevation

80°

150°

60°

30°

None

22.

From a point on the ground, the angles of elevation of the bottom and the top of a tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

Topic: Properties of Height

60 (√3 -1) m

20 (√3 -1) m

30 (√3 -1) m

40 (√3 - 1) m

None

23.

Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him at an elevation of 30°. Deepak standing on the roof of a 50 m high building, finds the angle of elevation of the same bird to be 45°. Amit and Deepak are on opposite sides of the bird. Find the distance of the bird from Deepak.

Topic: Properties of Distance

50√3 m

80√2 m

50√2 m

61√2 m

None

24.

A ladder 15 m long makes an angle of 60° with the wall. Find the height of the point where the ladder touches the wall.

Topic: Properties of Height

9.5 m

6.5 m

8.5 m

7.5 m

None

25.

An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?

Topic: Properties of Height

60 m

90 m

50 m

30 m

None

1 out of 25

Time's up

Class 10 Practice – Level 2 – Set 2 – Some Application of Trigonometry

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